Question

7. The area of a rhombus is equal to the area of a triangle whose base and corresponding altitude
are 30 cm and 16 cm, respectively. If one of the diagonals of the rhombus is 20 cm, find the
length of the other diagonal.​

Answer 1

Given

• Area of Rhombus = Area of Triangle.
• Base = 30 cm
• Height = 16 cm
• One of the Diagonals of Rhombus = 20 cm

______________________________

To Find

• The length of the other diagonal

______________________________

Solution

Since we know the area of triangle and rhombus is equal, we will recall the formula to obtain the area of triangle and rhombus respectively.

Area of Triangle ⇒ $\sf \frac{1}{2} \times Base\times Height$

Area of Rhombus ⇒ $\sf Diagonal\ 1\times Diagonal \ 2\times \frac{1}{2}$

Here let us consider the Diagonal 2 to be 'x'.

Now let's solve an equation to find the value of d₂

⇒ $\dfrac{1}{2} \times 30 \times 16 = \dfrac{1}{2} \times 20 \times x$

Let's multiply and bring the equation to simpler form.

⇒ $\dfrac{1}{2} \times 480 = \dfrac{1}{2} \times 20x$

⇒ $\dfrac{1}{2\div 2 } \times 480\div 2 = \dfrac{1}{2} \times 20x$

⇒ $240 = \dfrac{1}{2} \times 20x$

⇒ $240 = \dfrac{1}{2\div 2 } \times 20\div 2$

⇒ $240 = 10x$

Now we will flip the equation.

⇒ $10x=240$

Now we shall divide 10 from both sides of the equation.

⇒ $\dfrac{10x}{10} =\dfrac{240}{10}$

⇒ $x = 24$

∴ The length of the other diagonal is 24 cm

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Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

The area of a rhombus is equal to the area of a triangle whose base and corresponding altitude are 30 cm and 16 cm, respectively. If one of the diagonals of the rhombus is 20 cm, find the length of the other diagonal.

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• Area of a rhombus is equal to the area of a triangle.
• Base = 30 cm
• Altitude = 16 cm

$\large\purple{\texttt{Altitude means height}}$

• One of the diagonals of the rhombus = 20 cm

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• The length of the other diagonal.

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

• The length of the other diagonal = 24 cm

${\bigstar}\large{\boxed{\sf{\pink{Full \: solution}}}}$

According to the question we know that { Given } Area of a rhombus is equal to the area of a triangle. So, lets know what is the formula of area of triangle nd area of rohmbus.

$\large\green{\texttt{Area of triangle}}$

$\large{\boxed{\sf{1/2 × b × h}}}$

$\large\green{\texttt{Area of rohmbus}}$

$\large{\boxed{\sf{Diagonal 1 \: × \: Diagonal 2 \: × \: 1/2}}}$

$\mapsto$ Diagonal 2 isn't given . So let's Diagonal 2 be x.

$\large\green{\texttt{Substituting the value we get following results}}$

$\mapsto$ 1/2 × 30 × 16 = 1/2 × 20 × x

$\mapsto$ 1/2 × 480 = 1/2 × 20x

{ We get 480 & 20x bcz we multiply 30 by 16 & 20 by x }

$\mapsto$ 1 × 240 = 1 × 10x

{ We get above result bcz we divide 480 by 2 & 20x by 2 }

$\large\green{\texttt{Hence, we get equation 240 = 10x}}$

Continuing.....

$\mapsto$ 10x = 240

$\mapsto$ x = 240/10

$\mapsto$ x = 24

{ We get 24 bcz we cancel 0 by 0 like this – 240 / 10 = 24 / 1 = 24 }

$\implies$ $\large{\boxed{\sf{24 \: is \: the \: Answer}}}$

@Itzbeautyqueen23

Hope it's helpful

Thank you :)